VII. On the OniciIN and InveEsTIGATION of Portsms. By 
Foun PLarralR, F.R.S. Epin. and Profeffor of Ma- 
thematics in the Univerfity of EDINBURGH. 
BP) tAgiRy) re I. 
[Read April 2. 1792.] 
re HE reftoration of the ancient books of geometry would 
have been impoflible, without the coincidence of two 
circumftances, of which, though the one is purely accidental, 
the other is effentially connected with the nature of the mathe- 
matical fciences. The firft of thefe circumftances is the pre- 
fervation of a fhort abftract of thofe books, drawn up by 
Pappus ALEXANDRINUS, together with a feries of fuch /em- 
mata, as he judged ufeful to facilitate the ftudy of them. The 
fecond is, the neceffary connection that takes place among the 
objects of every mathematical work, which, by excluding what- 
ever is arbitrary, makes it poflible to determine the whole 
courfe of an inveftigation, when only a few points in it are 
known. From the union of thefe circumftances, mathematics 
has enjoyed an advantage of which no other branch of know- 
ledge can partake ; and while the critic or the hiftorian has 
only been able to lament the fate of thofe books of Livy and 
Tacitus which are loft, the geometer has had the high fatis- 
faction to behold the works of Euctip and APOLLONIUs re- 
viving under his hands. 
2. Tue firft reftorers of the ancient books were not, how- 
ever, aware of the full extent of the work which they had un- 
fsteyhs dertaken. 
